Charge recycling and adiabatic charging are two circuit technologies that can be employed to reduce the energy dissipated by an integrated circuit. These techniques are particularly useful in charging and discharging large capacitive loads or where the charging is performed in a cyclical fashion.
Conventional Charging
A large contribution to the total energy dissipated by an integrated circuit is the result of the charging and discharging of capacitive signal nodes within the circuit. This effect can be understood through the examination of a simple CMOS inverter as illustrated in FIG. 1.
Initially, the voltage across the capacitor 18 is zero and no energy is stored in the capacitor. The input signal 12 turns the P-channel MOSFET 14 off, and turns the N-channel MOSFET 16 on which grounds capacitor 18. When it is time to charge the capacitor 18, the P-channel MOSFET 14 conducts allowing current to flow from the power supply into the capacitor 18. Once the P-channel MOSFET 14 is conducting, the circuit can be modeled as a simple RC circuit 20 as illustrated in FIG. 2 which shows a power supply 22 supplying power to resistor 24 and capacitor 26. The RC circuit has the value of the resistor 24 as the “on” resistance of the MOSFET.
The energy dissipated in the circuit is the result of the current i(t) flowing through resistor 24 and is given by:
                              E          diss                =                              ∫            0            ∞                    ⁢                                                    i                2                            ⁡                              (                t                )                                      ⁢            R            ⁢                                                  ⁢                          ⅆ              t                                                          (        1        )            
The current flowing through the resistor 24 is the same as that flowing through the capacitor 26, which is given by:
                              i          ⁡                      (            t            )                          =                  C          ⁢                                    ⅆ                                                V                  c                                ⁡                                  (                  t                  )                                                                    ⅆ              t                                                          (        2        )            
Combining equations 1 and 2 and solving the resulting expression, it can be seen that the energy dissipated in the resistance is ½ CV2. It is important to note that due to charging with a constant voltage, the dissipation through the resistor is independent of the value of the resistor.
The charge necessary to charge the capacitor to the supply potential is equal to CV. This implies a total energy removed from the power supply is CV2. However, the charge is delivered through the resistor R and, as indicated above, the energy dissipated through the resistor is ½ CV2. Thus, one half of the energy removed from the power supply is dissipated in the resistor as heat, the other half going to charging the load.
When the load is discharged, i.e., the N-channel MOSFET conducts and discharges the capacitor to ground, a similar phenomenon occurs and another ½ CV2 is dissipated in the resistance of the N-channel MOSFET.
In the conventional case, both the charging and discharging of the signal node capacitance results in a dissipation of ½ CV2. All of the energy sourced from the power supply is eventually converted to heat in the resistances.
Adiabatic Charging
In thermodynamics, when a process does not transfer heat to the working fluid, it is referred to as being adiabatic. This concept can be extended into electronics and specifically into the charging of signal nodes within an integrated circuit. If a signal node can be charged or discharged without dissipating energy in the resistance, then the charging process is adiabatic.
To realize an adiabatic charging process, it is necessary to have more precise control of how the capacitive load is charged over time. This can be achieved by using a time-varying power supply that starts at zero and ramps over time towards the desired supply voltage as illustrated in FIG. 3. The linear voltage ramps provides a constant current and limits the voltage across the resistance to an arbitrarily small level. The energy dissipated in the resistor is given by:
                                          E            diss                    ⁡                      (                          RC              T                        )                          ⁢                  CV          dd          2                                    (        3        )            
It is evident from equation 3 that the energy dissipated in the resistor for this charging scenario is a function of the period of the time-varying supply. Increasing the period results in less dissipated energy and, in the case where T>>RC, the dissipation approaches zero. With the use of a decreasing voltage ramp, the load capacitance can be discharged in an adiabatic fashion which results in the same expression for the energy dissipated.
When adiabatic charging and discharging are used together, the reduction in dissipated energy can be dramatic. Referring to FIG. 4, consider the case of a capacitive load in circuit 40 that has been discharged to ground at time t0. For the example, it is assumed that the voltage source 42 is like an energy reservoir 41 storing CV2 of energy and the capacitor 46 is like an empty energy reservoir 48 with the circuit 40 having the resistor 44.
In FIG. 5, When the capacitive load is charged, ½ CV2 is delivered to the energy reservoir 58 that is the capacitor 56. Another RC/T CV2 has been removed from the power supply reservoir 51 and dissipated as heat in resistor 54 in accordance with equation 3. Thus, a total of (½+RC/T)CV2 is removed from the power supply reservoir 51 contrasted with the conventional charging case where the entire supply reservoir is emptied. When the load is discharged, another RC/T CV2 is dissipated in resistor 54 as the energy is returned to the supply reservoir 51 leaving a total of CV2−2RC/T CV2 in the supply 51 compared to the case of conventional charging where the supply reservoir is completely drained. In the limiting case where T>>RC, the circuit dissipates no energy in the resistor, and the charge drawn from the power supply to charge the capacitor is returned to the power supply when the capacitor is discharged.
Ordinary power supplies are incapable of dealing with the charge returned during an adiabatic discharge as it is usually dissipated to ground through a shunt impedance. This limitation renders the adiabatic discharging process no more efficient than the conventional discharging method. In order to take advantage of the of the returned energy, it is necessary to use a resonant source for the time-varying power supply as it is capable of reclaiming the returned charge, storing it, and making it available for use in subsequent clock cycles.